Hey guys, Thanks for all of the advice.
I read the safemode thing before the reinstall / uninstall thing, so I tried that first. No luck. I couldn't find any trace of the program where you said to look, which is very strange since it was still trying to run in normal boot mode! I also cleared my start up folder in the start menu, which did nothing. Finally, after rebooting in normal mode, I decided to just type the path given on the error in my start menu search and see what came up. I had already searched for WinZip before this and got nothing, but after following the exact path, I could see a folder for this program still on my computer. I deleted it and the 132 items it contained, and now it's truly gone!
Now after reviewing this thread, I'm sure that if I just reinstalled it then uninstalled it that would have worked and been MUCH easier and quicker, but done is done I suppose lol. Thanks guys.